论文标题
椭圆曲线的杂音
Murmurations of elliptic curves
论文作者
论文摘要
我们研究了P在P上的Frobenius Trace的平均值，而椭圆曲线的固定导体范围为给定等级。绘制该平均值随着P的变化而变化会产生惊人的振荡模式，其细节随级别而变化。基于此观察结果，我们执行各种数据科学实验，目的是根据其等级对椭圆曲线进行分类。
We investigate the average value of the Frobenius trace at p over elliptic curves in a fixed conductor range with given rank. Plotting this average as p varies over the primes yields a striking oscillating pattern, the details of which vary with the rank. Based on this observation, we perform various data-scientific experiments with the goal of classifying elliptic curves according to their ranks.
